Mu'tazz
Yes. Mu'tazz is historically attested; most notably it was used as the regnal name of the Abbasid caliph al-Mu'tazz (reigned 866–869 CE).
Derived from the Arabic root ع-ز-ز, Mu'tazz is understood as 'the strengthened one' or 'one who takes strength/pride', often interpreted theologically as 'strengthened (by God)'.
No. The name Mu'tazz does not occur in the Quran; its attestations are in historical and administrative records of the medieval Islamic period.
Yes, though it is rare in contemporary naming practices. It carries classical connotations and historical resonance (particularly Abbasid-era).
A common transliteration is 'Mu'-tazz' pronounced approximately as 'moo-TAAZ-z' (/muʔtˈazz/), with a glottal stop after the 'Mu'.